Summary

Model v0.2.6 was created using sst, chl, bat, sss, wind, lag_sst, int_chl, slope, bott, bots, dist for cfin. The models were averaged into climatologies with one climatology per month. Evaluations were compiled from the climatological averages and plotted. Finally, the study area was divided up into three regions, the Mid-Atlantic Bight (MAB), George’s Bank (GBK), and the Gulf of Maine (GOM). Actual versus predicted abundance values were plotted for each region. The mgvc GAMs and the gbm BRTs were run using the CPR, NOAA_CPR dataset(s). The Biomod2 models were run using the `` dataset(s). If the model is an anomaly, all datasets are used.

Climatologies

GAM Climatology

The generalized additive models (GAMs) were run using the mgcv package and were used to model cfin abundances.

Figure 1. Monthly climatological GAM projections. The climatology was created by averaging together the projections from 2000 to 2017.

BRT Climatology

The boosted regression tree (BRT) models were run using the gbm package and used to model cfin abundances.

Figure 2. Monthly climatological BRT projections. The climatology was created by averaging together the projections from 2000 to 2017.

Biomod Ensemble Climatology

The ensemble models were created using the biomod2 package. The ensembles consist of BRTs, GAMs, and random forests (RFs). The ensembles were used to model the right whale feeding threshold, with any abundance greater than 4\times 10^{4} cfin per \(m^3\) counted as a presence and anything below that threshold counted as an absence.

Figure 3. Monthly climatological ensemble projections of GAMs, BRTs, and random forests (RFs). The climatology was created by averaging together the projections from 2000 to 2017.

Biomod GAM Climatology

The GAM models created with biomod2 were used to model the right whale feeding threshold, with any abundance greater than 4\times 10^{4} cfin per \(m^3\) counted as a presence and anything below that threshold counted as an absence.

Figure 4. Monthly climatological GAM projections produced using Biomod2. The climatology was created by averaging together the projections from 2000 to 2017.

Monthly ensemble projections

Monthly ensemble Biomod2 projections are displayed below for the months of May, June, July, August, and September.

April

Figure 5. Ensemble projections for the month of April over 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017.

May

Figure 6. Ensemble projections for the month of May over 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017.

June

Figure 7. Ensemble projections for the month of June over 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017.

August

Figure 8. Ensemble projections for the month of August over 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017.

September

Figure 9. Ensemble projections for the month of September over 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017.

Evaluations

Evaluation metrics differed based on the metrics available in each modeling package and compatible with each model object. For the mgcv GAMs, Aikaike’s Information Criterion (AIC), the root mean squared error (RMSE), and the R squared (RSQ) value when comparing the actual and predicted abundances were computed. For the BRTs produced using the gbm package, RMSE and RSQ were computed. For the biomod2 ensembles and GAMs, the area under the receiver operator characteristic curve (AUC) and the true skill statistic (TSS) were computed.

GAM evaluations

Figure 10. Model evaluations on a monthly time scale using a.) AIC, b.) RMSE, and c.) R2.

BRT evaluations

Figure 11. Model evaluations on a monthly time scale using a.) RMSE and b.) R2.

Biomod ensemble evaluations

Figure 12. Biomod ensemble evaluations on a monthly time scale using a.) AUC and b.) TSS

Biomod GAM evaluations

Figure 13. Biomod GAM evaluations on a monthly time scale using a.) AUC and b.) TSS

Regions

The study area was divided into three regions, the MAB, GBK, and GOM. For each region, a climatological average (one point per month), monthly average time series, and annual average time series were computed and the actual versus predicted abundance values were plotted. So far, this has only been done for the mgcv GAMs and gbm BRTs.

GAM regions

Climatological average

Figure 14. Climatological abundance values averaged over three regions, a.) the Mid Atlantic Bight, b.) George’s Bank, and c.) the Gulf of Maine. The predicted values come from the projections.

Monthly average time series

Figure 15. Abundance values averaged monthly over three regions, a.) the Mid Atlantic Bight, b.) George’s Bank, and c.) the Gulf of Maine. The predicted values come from the projections.

Monthly average time series

Figure 16. Abundance values averaged annually over three regions, a.) the Mid Atlantic Bight, b.) George’s Bank, and c.) the Gulf of Maine. The predicted values come from the projections.

BRT regions

Climatological average

Figure 17. Climatological abundance values averaged over three regions, a.) the Mid Atlantic Bight, b.) George’s Bank, and c.) the Gulf of Maine. The predicted values come from the projections.

Monthly average time series

Figure 18. Abundance values averaged monthly over three regions, a.) the Mid Atlantic Bight, b.) George’s Bank, and c.) the Gulf of Maine. The predicted values come from the projections.

Monthly average time series

Figure 19. Abundance values averaged annually over three regions, a.) the Mid Atlantic Bight, b.) George’s Bank, and c.) the Gulf of Maine. The predicted values come from the projections.

Actual abundance vs. predicted probability of suitability

For the biomod ensemble models, the logged actual abundance of cfin was plotted against the predicted probability of suitability. Above the threshold of 4\times 10^{4}, the probability of suitability tends to increase. Below the threshold, the probability of suitability tends to be zero.

Figure 20. Actual logged abundance versus predicted probability of suitability for cfin for all 12 months.